In the formation of glass fibers from molten glass streams supplied by a feeder or bushing, the attenuation of the streams into fibers and the packaging of the fibers as glass strand may be accomplished with a single-collet, dual-package winder. In such a system, the fibers from two halves of the bushing are gathered into two strands respectively by a pair of primary shoes after being drawn over a dual sizing applicator roll, or respectively over a pair of sizing applicator rolls, and the two strands are wound into two packages on the collet after passing respectively through a pair of secondary shoes and over a pair of conventional helical wire package builders. When the packages are complete, the operator shuts off the winder, breaks the strands from the completed packages, and inserts the strands from the primary shoes temporarily between a pair of pull rolls offset from the secondary shoes, thereby removing the strands from the secondary shoes. The pull rolls pull the fibers from the bushing to prevent flooding thereof and the scrap strand generated is fed to a lower level through a hole in the floor while the operator removes the completed packages from the collet and places empty paper tubes thereon. With the empty paper tubes in place, the operator turns on the winder, removes the strands from the pull rolls, and threads the strands temporarily into a groove on the front end of the collet until the linear speed of the strands is increased from the slow speed in the pull rolls to proper winding speed. Then the operator pushes the strands along the collet to move them respectively into operative engagement with the paper tubes and threads them respectively into the pair of secondary shoes above. Prior to our invention, to thread the rear strand into the rear secondary shoe, the operator had to lean dangerously close to the front of the rotating winding collet.